This is a Phase IB, open-label, dose-finding study of the JAK 1 and 2 inhibitor ruxolitinib in patients with myelofibrosis (MF). The study consists of two periods: the core study period, comprising the dose escalation stage and the safety extension phase up to Week 24, then the extension study period beyond Week 24 and up to 3 years, to further characterize the safety and efficacy of ruxolitinib in this patient population. The dose escalation phase will enroll successive cohorts of patients who receive increasing doses of ruxolitinib until the maximum safe starting dose (MSSD) is determined. In the safety expansion phase, additional patients will be treated with ruxolitinib at the MSSD defined during dose escalation. The primary objective is to establish the MSSD of ruxolitinib in patients with MF and starting platelet counts < 100 x 10 ^9/L